Our company is Beatrice Health, and our flagship product is called "Beatrice." We'd like a logo that is simple and elegant, modern but not flashy. It will need to be simple enough that some reduced (and perhaps simplified) version of it will work as an icon on an iPhone.
The name Beatrice of course evokes femininity. Because our application has to do with helping patients with dementia (and helping caregivers to help them), we'd like something feminine and personal (but, of course, not sexy or brash). Words that come to mind in the context of Beatrice: support, help, care, loving, nurturing, sympathy. Colors should also reflect this: probably reds and oranges should be avoided, given preference to calmer blues, greens, grays.
We'd like to give designers free rein to experiment, but we have attached an example of a logo we like a lot. It's the logo for the rapid transit system in Paris (the RATP), where the river is modified into the profile of a woman. It's one example of many of a logo that evokes femininity without being too explicit.